International
Tables for
Crystallography
Volume H
Powder diffraction
Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk

International Tables for Crystallography (2018). Vol. H, ch. 3.3, p. 265

Section 3.3.2.4. Fundamental parameters profile modelling

R. B. Von Dreelea*

aAdvanced Photon Source, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439–4814, USA
Correspondence e-mail: vondreele@anl.gov

3.3.2.4. Fundamental parameters profile modelling

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An alternative method for describing the source and instrumental part of the powder peak profile is to develop a set of individual functions that form the part of the profile arising from each of the instrumental components that shape the beam profile (Cheary & Coelho, 1992[link], 1998a[link],b[link]). Ideally, each function is parameterized in terms of the physical parameters of the corresponding instrument component (e.g. slit width and height, sample dimensions and absorption, source size and emission characteristics, etc.), which are known from direct measurement. The set of functions are then convoluted via fast mathematical procedures to produce a line profile that matches the observed one. Any remaining profile-broadening parameters (e.g. for sample crystallite size and microstrain, see Section 3.3.5[link] for details) are then allowed to adjust during a Rietveld refinement. By employing this fundamental parameters (FP) approach, these parameters are unaffected by any instrumental parameterization.

The FP method offers two clear advantages over the more empirical approach outlined in Sections 3.3.2.1[link]–3.3.2.3[link] above: (i) it can more closely describe the actual instrumental effects that contribute to the profile shape, thus improving the precision of the fit to the observed data and (ii) it can be used to describe a source characteristic or an instrumental arrangement that is outside the normally used configuration, yielding a result that would be difficult to obtain otherwise (Cheary et al., 2004[link]).

References

Cheary, R. W. & Coelho, A. A. (1998a). Axial divergence in a conventional X-ray powder diffractometer. I. Theoretical foundations. J. Appl. Cryst. 31, 851–861.Google Scholar
Cheary, R. W. & Coelho, A. A. (1998b). Axial divergence in a conventional X-ray powder diffractometer. II. Realization and evaluation in a fundamental-parameter profile fitting procedure. J. Appl. Cryst. 31, 862–868.Google Scholar
Cheary, R. W. & Coelho, A. (1992). A fundamental parameters approach to X-ray line-profile fitting. J. Appl. Cryst. 25, 109–121.Google Scholar
Cheary, R. W., Coelho, A. A. & Cline, J. P. (2004). Fundamental parameters line profile fitting in laboratory diffractometers. J. Res. Natl Inst. Stand. Technol. 109, 1–25.Google Scholar








































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